Approximate linearization by state feedback and coordinate change

Abstract

A nonlinear system can always be approximated to first order by linear systems. It has been shown by Jakubczyk and Respondek [4] and Hunt and Su [3] that certain nonlinear systems are the exact transforms of linear systems under nonlinear state coordinate change and nonlinear state feedback. In this paper we give necessary and sufficient conditions for a nonlinear system to be approximated to higher order by the transform of a linear system. The use of this technique in the design of nonlinear compensators has been suggested recently by the author [6]. © 1984 Elsevier Science Publishers B.V.